and many more benefits!

Find us on Facebook

GMAT Club Timer Informer

Hi GMATClubber!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

M approach to mixture problems is like this: Suppose we work [#permalink]

Show Tags

08 Aug 2008, 09:22

1

This post wasBOOKMARKED

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

M approach to mixture problems is like this:

Suppose we work in a science lab and need a mixture of acid of 20%. The we look in the supply closet and find 10% and 35% mixtures of the same acid. We're smart people, WE ARE SCIENTISTS after all, so we decide to mix up our own 20% mixture with what we have.

Lets say we have acid mixed with water to make our mixture. If we have a 10% mixture and we have 10 litres of that mixture. That means there is 1 litres of acid and 9 liters of water.

There are 2 approaches. One is slow, but easier to follow and less abstract, and the other involves the formulas.

I do not recommend the slow way. It's just that slow, and no good on the GMAT.

Equation MethodLet a = total liters of 10% mixtureLet b = total liters of 35% mixture

Total liters of of pure acid will be .1a and .35b.(Note: the ---- is just there to keep spacing.)It helps to organize this into a table-----------Liters Solution-------Percent Acid-------Pure Acid in terms of variable10% Sol.-------x--------------------10%---------------------.1x35% sol.-------y--------------------35%---------------------.35yDesired--------10-------------------20%-----------------(0.2)(10) = 2

We have 2 variables. We need to solve for one of them and then that value will lead to the overall answer.

This tells us that when we have a 10% mixture of acid added to a 30% mixture of acid to get 10 liters, we need 4 liters of y (the 35% mixture) and 6 liters of x (10-y; the 10%) solution.

I highly suggest the table method as it helps you separate out and label everything. Organization is key to a problem like this because when you get to y = 4, you need to know what that really means because you're not done with the problem!

you also might see the question in DS form:

Do you have enough 10% and 35% mixture to make 10 gallons of 20% mixture?1) You have 6 gallons of 10% mixture2) You have half as much 35% mixture as 10% mixture.

The same process applies, but your answer will be in a different form. Yes/No.

EDIT: I just realized I provided the easiest DS question in the history of DS quesions. If you have 6 gallons, you don't know how much 35% you have. It's clear that alone the statements are insufficient. Together, it shows that you have 9 gallons! You don't need to do any calculations. If you're asked if you have enough to make 10 gallons of mixture and all you have it a total of 9....who needs to compute % ? LOL
_________________

------------------------------------J Allen Morris**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

Show Tags

08 Aug 2008, 09:41

allen , there is also a simpler procedure..0.1a+.35b=.2(a+b).or a/b=1.5/1.so we clever scientists mix the mixture(i prefer if there was alchol... my stomach would have been an additional container to mix ) in the ratio of 1.5:1 or in other words, the same that you have arrived at 4 and 6(since 6/4=1.5)....

Show Tags

08 Aug 2008, 09:49

jallenmorris wrote:

EDIT: I just realized I provided the easiest DS question in the history of DS quesions. If you have 6 gallons, you don't know how much 35% you have. It's clear that alone the statements are insufficient. Together, it shows that you have 9 gallons! You don't need to do any calculations. If you're asked if you have enough to make 10 gallons of mixture and all you have it a total of 9....who needs to compute % ? LOL

you can complicate the question by adding "Assume that you have enough water available"

Show Tags

08 Aug 2008, 10:00

1

This post receivedKUDOS

I was originally posting this for leonidas as (s)he had asked for information regarding mixture problems. Thanks for the clarification on the simpler formula. I thought of that, but wasn't sure it would work. I had seen the table method somewhere when I was learning it myself. The table method does help if someone is a very visual person, but the .1a + .35b = .2(a+b) is good to. As long as the person can then apply the ratio to get the needed volume.

1:1.5...2:3=5 4:6 = 10...there it is. It's just a matter of being able to recognize what information is present and what needs to be done to get that information into the correct format for the answer.
_________________

------------------------------------J Allen Morris**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

Show Tags

08 Aug 2008, 11:06

Allen and arjtryarjtry. Appreciate your responses to my request.

Allen, I also found this piece (attachment) that follows the table approach. I am positing this for folks who might want to see other examples. This also seperates in terms of dry mixture and chemical mixture problems.

Attachments

chemical Mixtures.JPG [ 68.74 KiB | Viewed 2117 times ]

Dry mixture.JPG [ 71.63 KiB | Viewed 2108 times ]

_________________

To find what you seek in the road of life, the best proverb of all is that which says:"Leave no stone unturned." -Edward Bulwer Lytton

Last edited by leonidas on 08 Aug 2008, 11:13, edited 1 time in total.

Allen, I also found this piece (attachment) that follows the table approach. I am positing this for folks who might want to see other examples. This also seperates in terms of dry mixture and chemical mixture problems.

_________________

------------------------------------J Allen Morris**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

Show Tags

08 Aug 2008, 11:29

Purplemath website is very good. Mostly it is basic stuff, however, that's the kind of foundation one needs for GMAT. I grew up doing differentiations and integrations (advanced math), but my basic skills used to be very average. I am now re-visiting what I learnt in my 6th grade to 10th grade _________________

To find what you seek in the road of life, the best proverb of all is that which says:"Leave no stone unturned." -Edward Bulwer Lytton